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Question
The following table shows the age distribution of head of the families in a certain country. Determine the third, fifth and eighth decile of the distribution graphically.
| Age of head of family (in years) |
Numbers (million) |
| Under 35 | 46 |
| 35 – 45 | 85 |
| 45 – 55 | 64 |
| 55 – 65 | 75 |
| 65 – 75 | 90 |
| 75 and Above | 40 |
Solution
To draw a ogive curve, we construct a less than cumulative frequency table as given below:
| Age of head of family (in years) |
Numbers (million) (f) |
Less than cumulative frequency (c.f.) |
| Under 35 | 46 | 46 |
| 35 – 45 | 85 | 131 |
| 45 – 55 | 64 | 195 |
| 55 – 65 | 75 | 270 |
| 65 – 75 | 90 | 360 |
| 75 and Above | 40 | 400 |
| Total | 400 |
Points to be plotted are (35, 46), (45, 131), (55, 195), (65, 270), (75, 360), (85, 400).
N = 400
For D3, we have to consider `(3"N")/(10)=(3(400))/(10)` = 120,
For D5, we have to consider `(5"N")/(10)=(5(400))/(10)` = 200
For D8, we have to consider `(8"N")/(10)=(8(400))/(10)` = 320
∴ We consider the values 120, 200, and 320 on Y-axis. From these points, we draw the lines parallel to X-axis. From the points where they intersect the less than ogive, we draw perpendiculars on the X-axis. The foot of the perpendicular represents the values of D3, D5, and D8.
∴ D3 ≈ 44, D5 ≈ 55.5, and D8 ≈ 70
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